Patterns of Non-exponential Growth of Macroeconomic Models: Two-parameter Poisson-Dirichlet Models

We investigate the structure of interactions among countries exercising voluntary uncoordinated choice but sharing a common "risk profile" --- a vector comprised of chance of adversity/emergency and magnitude of loss under adversity/emergency. We use the term "emergency costs" to refer to the vector and/or its components. Countries strive to reduce emergency costs (a) by providing mutual self-insurance against loss and (b) mutual self-protection against risk. Because of their common risk profile each country's security spending whether on self-insurance or on self-protection provides a public good (pure or impure) to all in the group --- hence our term "mutual." We show that under expected utility maximization the normality or inferiority of such public goods depends crucially on hitherto unrecognized interactions between preference functions and status quo risks. Moreover we discover that these interactions differ systematically between insurance and protection with important policy implications for comparing the two instruments. Furthermore, we demonstrate that configurations where security is inferior are not at all unlikely. In such case the provision of international public goods can easily face an endogenous obstacle, an "inferior good barrier," under Nash-Cournot behavior and under Leader-Follower behavior with Stackelberg outcomes. (These, however, display novel and desirable properties even when the public good is inferior.) When improvements in risk profile generate not pure public goods, but instead imperfect, ambiguous, or even negative benefits among partners, who is an ally and who an adversary, itself becomes ambiguous. For this configuration where the emergency risk profile differs among allies, we show how spillovers from emergency cost reduction and their effects on welfare will be depend critically on the sign of income effects.